A golfer hits a golf ball, giving it an initial speed of 39.7 m/s at an angle of 55° above the horizontal. What is the maximum height in meters that the golf ball will achieve?
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To find the maximum height that the golf ball will achieve, we can use the kinematic equations of motion and the vertical component of the initial velocity.
Step 1: Break down the initial velocity vector into its horizontal and vertical components.
The vertical component can be calculated using the formula V_y = V_initial * sin(theta), where V_y is the vertical component and theta is the angle above the horizontal.
V_y = 39.7 m/s * sin(55°)
V_y ≈ 32.50 m/s
Step 2: Determine the time it takes for the ball to reach its maximum height.
The time it takes for the ball to reach its maximum height is half of the total time of flight since the motion is symmetrical. The total time of flight can be calculated using the formula T = (2 * V_y) / g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
T = (2 * 32.50 m/s) / 9.8 m/s^2
T ≈ 6.63 s
The time it takes for the ball to reach its maximum height is half of this value: t = T / 2 = 6.63 s / 2 = 3.32 s.
Step 3: Calculate the maximum height.
The maximum height can be calculated using the formula H_max = V_y * t - (1/2) * g * t^2, where H_max is the maximum height and t is the time calculated in Step 2.
H_max = (32.50 m/s) * (3.32 s) - (1/2) * (9.8 m/s^2) * (3.32 s)^2
H_max ≈ 54.40 m
Therefore, the maximum height that the golf ball will achieve is approximately 54.40 meters.
Vo = 39.7m/s[55o]
Yo = 39.7*sin55 = 32.52 m/s. = Vertical component.
Y^2 = Yo^2 + 2g*h
h = (Y^2-Yo^2)/2g = (0-(32.52^2)/-19.6 =
54 m.